(s)-nuclear sets and operators

Kari Astala and M. S. Ramanujan

Vol. 127 (1987), No. 2, 233–246

DOI: 10.2140/pjm.1987.127.233

Abstract

The purpose of this paper is to demonstrate considerable similarities in the behaviour of compact and (s)-nuclear operators. More precisely, we obtain for (s)-nuclear operators results resembling previously known properties of compact operators; sometimes a word for word translation of a “compact theorem” holds for (s)-nuclear operators. However, we wish to emphasize that different methods for the proofs are now needed. For example, the often applied Ascoli-Arzela theorem does not have a (s)-nuclear counterpart (see §5).

Mathematical Subject Classification 2000

Primary: 47B10

Secondary: 47D30

Milestones

Received: 9 July 1985

Revised: 22 August 1986

Published: 1 April 1987